# Properties

 Label 800.2.bp Level $800$ Weight $2$ Character orbit 800.bp Rep. character $\chi_{800}(47,\cdot)$ Character field $\Q(\zeta_{20})$ Dimension $224$ Newform subspaces $3$ Sturm bound $240$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$800 = 2^{5} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 800.bp (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$200$$ Character field: $$\Q(\zeta_{20})$$ Newform subspaces: $$3$$ Sturm bound: $$240$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(800, [\chi])$$.

Total New Old
Modular forms 1024 256 768
Cusp forms 896 224 672
Eisenstein series 128 32 96

## Trace form

 $$224q + 16q^{3} - 20q^{9} + O(q^{10})$$ $$224q + 16q^{3} - 20q^{9} + 12q^{11} - 12q^{17} + 20q^{19} - 20q^{25} + 28q^{27} - 4q^{33} + 40q^{35} - 12q^{41} + 48q^{43} + 32q^{51} - 28q^{57} + 20q^{59} - 20q^{65} - 8q^{67} - 36q^{73} - 40q^{75} + 12q^{81} - 24q^{83} - 120q^{89} + 12q^{91} + 44q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(800, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
800.2.bp.a $$8$$ $$6.388$$ $$\Q(\zeta_{20})$$ None $$0$$ $$0$$ $$-10$$ $$4$$ $$q+(-1+\zeta_{20}+\zeta_{20}^{2}-2\zeta_{20}^{3}-2\zeta_{20}^{4}+\cdots)q^{3}+\cdots$$
800.2.bp.b $$8$$ $$6.388$$ $$\Q(\zeta_{20})$$ None $$0$$ $$0$$ $$10$$ $$-4$$ $$q+(-1+\zeta_{20}+\zeta_{20}^{2}-2\zeta_{20}^{3}-2\zeta_{20}^{4}+\cdots)q^{3}+\cdots$$
800.2.bp.c $$208$$ $$6.388$$ None $$0$$ $$16$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(800, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(800, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(200, [\chi])$$$$^{\oplus 3}$$